Chapter 8.6, Problem 9E

Interpretation Introduction

Interpretation:

To analyse the Japanese tree frog system and:

• (a) To write the system in terms of the phase differences.

• (b) To show that the experimental result is consistent with the interaction function $\text{H(x)}=\text{ a sin(x)}$, but this cannot account for the three frog system.

• (c) To show that the more complicated form of the interaction function $\text{H(x)}=\text{ a sin(x)+ b sin(2x)}$ is obeyed by the three frog system.

• To plot the phase portraits of the three frog system in terms of the phase differences and explain the experimental results in two or three systems for the various parameter values.

• (e) To show that adding a small, even periodic component to H does not alter the result qualitatively.

Concept Introduction:

• ➢ The fixed point of a differential equation is the point where, $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$.

• ➢ The phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, whether they will attract or repel the flow, etc.